Pulse-tube refrigerators are robust and reliable devices for providing cryogenic refrigeration powered by acoustic energy. A traditional single-stage pulse-tube refrigerator (PTR) 1, shown in FIG. 1, comprises a sealed volume filled with a thermodynamic working fluid, typically high pressure helium gas. Inside the sealed volume is a Stirling thermodynamic unit (STU) 2 consisting of a main ambient heat exchanger 3, a regenerator 13, and a cold heat exchanger 5. The remainder of the sealed volume includes a thermal buffer tube (TBT) 11, an acoustic network 9, and secondary ambient heat exchanger 15. The main ambient heat exchanger 3 allows waste heat to exit the STU 2 at ambient temperature, while the refrigeration load enters the STU 2 via the cold heat exchanger 5 from a lower temperature heat source or cooled space or substance. Those skilled in the art will recognize that a refrigerator can also operate as a heat pump where the heat rejection, which is the desired output of the heat pump, takes place at heat exchanger 3 at a temperature higher than ambient. The STU 2 is driven by some form of acoustic wave generator 7, for example, an electrodynamic linear compressor or a thermoacoustic engine, which launches a high-amplitude acoustic wave into the STU 2 near the main ambient heat exchanger 3 (often called the aftercooler in the pulse tube refrigerator literature). For a given oscillatory pressure amplitude generated by the acoustic wave generator 7, the oscillatory volume flow rate amplitude and time phasing relative to the acoustic pressure is mainly set by the acoustic impedance of the acoustic network 9 extending away from the ambient end of the TBT 11 (described below). In typical STU's, the time phase of the complex volumetric flow rate amplitude U1 at the main ambient heat exchanger 3 leads the phase of the complex pressure amplitude p1 by anywhere from 0 to 50 degrees. In between the main ambient heat exchanger 3 and cold heat exchanger 5 is a regenerator 13 where the pressure and displacement oscillations in the acoustic wave produce the STU's 2 cooling power by pumping heat from the cold heat exchanger 5 to the main ambient heat exchanger 3. During this process, some of the acoustic power contained in the wave is consumed. However, there is a significant amount of residual acoustic power that flows away from the STU 2 through the cold heat exchanger 5.
After the cold heat exchanger 5 is the TBT 11 whose role is to allow the acoustic wave (and the residual acoustic power carried by that wave) to propagate away from the cold heat exchanger 5 and to ambient temperature while thermally isolating the STU's cold heat exchanger 5 from ambient temperature. Following the TBT 11 is an ambient temperature acoustic network 9 that provides an acoustic termination for the PTR 1 and dissipates the residual acoustic power carried by the wave. The intervening secondary ambient heat exchanger 15 rejects the heat generated by the dissipation to ambient temperature. TBTs are susceptible to significant secondary flows due to potentially poorly distributed oscillating flows at their ends, e.g. jets emanating from cold heat exchanger 5 and secondary ambient heat exchanger 15. To minimize such secondary flows, flow straighteners may be placed at both ends of a TBT, but for clarity, they are not shown in the Figures.
Although PTRs are robust and reliable, they are inherently irreversible refrigerators because the residual acoustic power flowing from the cold heat exchanger 5 must be dissipated in the acoustic network 9 to provide appropriate acoustic conditions at the inlet to the STU 2 (near the main ambient heat exchanger 3). The recovery and useful application of this residual power are key to improving the efficiency of this refrigeration technique. The following describes some previously described means for recovering the residual power and increasing efficiency.
FIG. 2 shows a feedback pulse-tube refrigerator (FPTR) 21 (disclosed in U.S. Pat. No. 6,032,464), which comprises a lumped-element acoustic network (“network”) 27 consisting of a compliance volume 23 and inertance tube 25 (typically much shorter than a quarter of an acoustic wavelength in the working fluid) to recycle the residual acoustic power back to the main ambient heat exchanger 3. Because of the acoustic properties of the network 27, the left-right order of the main ambient heat exchanger 3 and the cold heat exchanger 5 and regenerator 13 in the STU 2 are reversed in FIG. 2 relative to FIG. 1; however, they are in the same order with respect to the flow of acoustic power E. There are no moving parts required, as the acoustic power is simply transmitted using open ductwork. One limitation of this design is that the closed loop formed by the network 27, the STU 2, and the TBT 11 opens up a path for acoustic streaming, i.e. a second-order steady flow generated by the first-order acoustic oscillation. If unchecked, this steady flow may carry a heat leak. A fluid diode can be used to suppress this flow, but this technique may be unstable and thus unsuitable for many operating conditions. Alternately a membrane or bellows-like device can be placed in the ductwork to block the steady flow while allowing the first-order oscillating flow to pass. However, the introduction of moving mechanical components may reduce the reliability of the FPTR 21. An additional limitation arises for large FPTRs. When FPTRs are scaled up in cooling power, the cross-sectional areas of the STU 2, the TBT 11, and the secondary ambient heat exchanger 15 grow in proportion to the cooling power, whereas the lengths of the individual components remain relatively unchanged. The network 27 that recycles the acoustic power back to the main ambient heat exchanger 3 also grows in diameter while its length remains relatively unchanged. When the diameters become comparable to the lengths, connecting the ends of the network 27 to the STU 2 and the secondary ambient heat exchanger 15 becomes problematic, requiring extra length in the connections, causing extra dissipation of acoustic power due to sharp corners, and/or exacerbating flow-straightening problems at the ambient end of the TBT 11.
A related technique, shown in FIG. 3, utilizes a much longer, approximately half-wavelength-long feedback tube 31 to recycle the acoustic power from the ambient end of the FPTR's TBT 11 to the backside of the linear compressor's piston 33. If the FPTR 30 were driven by a thermoacoustic engine, the tube would rejoin the thermoacoustic engine/resonator system approximately half of a wavelength away from the refrigerator's main ambient heat exchanger. By placing the half-wavelength-long feedback tube 31 after the TBT 11, the acoustic volume flow rate into the half-wavelength-long feedback tube 31 is quite large resulting in large gas velocities. Combined with the length of the half-wavelength-long feedback tube 31, the high gas velocities result in significant acoustic dissipation, which may negate much of the benefit of recycling the acoustic power. Furthermore, if used on a thermoacoustic engine/resonator system, the half-wavelength-long feedback tube 31 opens up a streaming path similar to the path of FIG. 2.
Another related technique, disclosed in U.S. Pat. No. 4,114,380, utilizes two half-wavelength-long tubes to couple the STU of an acoustic-traveling-wave engine to the STU of an acoustic-traveling-wave refrigerator. The two STUs and half-wavelength-long tubes form a one-wavelength-long loop with the STUs separated from each other by a half wavelength in either direction. The loop allows the residual acoustic power from the cold end of the refrigerator STU to flow into the ambient end of the engine STU to be amplified and sent back to the ambient end of the refrigerator STU. One limitation of this technique is that the loop creates a path for streaming that decreases the performance of both the engine and refrigerator STUs. Another limitation of this technique is that the acoustic gain of the engine STU must be balanced by the acoustic attenuation of the refrigerator STU making control of the refrigerator STU's cold-end temperature dependent on the hot-end temperature of the engine STU.
Yet another technique, shown in FIG. 4, places an electrodynamic linear alternator 41 at some distance past the STU 2. The electrodynamic linear alternator 41 converts the previously dissipated acoustic power back into electricity that can be used to supply some of the electrical input to the acoustic wave generator 7. One limitation of this technique is that more moving components are introduced. In addition, the unit will also likely require electrical power conditioning equipment to make the phase of electrical power generated by the electrodynamic linear alternator 41 compatible with that required by the acoustic wave generator 7.
Yet another technique, disclosed in U.S. Pat. No. 6,658,862, is depicted in FIG. 5. In place of the acoustic network 9 of FIG. 1, a second-stage PTR 51 of smaller cross-sectional area is cascaded onto the ambient end of the TBT 11. The second-stage PTR 51 operates using the residual acoustic power from the first-stage STU 2. However, the phase relationship between the complex acoustic pressure amplitude p1 and the complex volumetric flow rate amplitude U1 at the input to the second-stage PTR 51 will not be optimal. If the first-stage STU 2 and the second-stage STU 64 operate at a cold-end temperature far from ambient, then the majority of the cooling power will be provided by the first-stage STU 2. Therefore, the acoustic pressure, volume flow rate, and the phase difference between them should be optimized for the operation of the first-stage STU 2. Typically this requires the acoustic volume flow rate phasor U1 at the first-stage main ambient heat exchanger 3 to lead the acoustic pressure phasor p1 in time phase by 0 to 50 degrees. After the acoustic wave has propagated through the first-stage STU 2 and TBT 11, the phase of U1 will be lagging p1 by 40-80 degrees which results in inefficient operation of the second-stage PTR 51. Any improvement in the acoustic input to the second stage will come at the expense of the efficiency of the first-stage STU 2 which is providing the majority of the cooling power and has a bigger effect on the overall system efficiency.
Yet another technique is shown in FIG. 6 and disclosed in U.S. Pat. No. 6,658,862. Instead of cascading a smaller PTR directly onto the end of a first-stage TBT 11, an intervening, approximately half-wavelength-long resonator 53 of roughly the same diameter as the first-stage STU 2 is used to modify the p1 and U1 phasors to values more favorable to second-stage PTR 51 performance. However, as discussed later in the detailed description of the present invention, the use of such a large diameter and length has several limitations, and causes the acoustic conditions at the inlet to the second-stage STU 64 to be very sensitive to the properties of the half-wavelength-long resonator 53 such as the temperature of the gas in the resonator. In addition, this technique leads to additional dissipation which can waste a significant fraction of the residual acoustic power exiting the first-stage STU 2.
For high power STUs, each of the aforementioned techniques has limitations in regard to the recovery or utilization of the residual acoustic power that flows away from STU 2: addition of moving mechanical components, creation of closed-loop streaming paths, the difficulty of designing smooth, compact ductwork paths from short, large-diameter piping, compromising the performance and efficiency of a first-stage refrigerator for the sake of adding a smaller, second stage, or excessive dissipation of first-stage residual acoustic power. A need exists, therefore, for a pulse-tube refrigerator which overcomes these limitations.